Classical Mechanics with Calculus of Variations and Optimal Control

Mark Levi

ISBN 10: 0821891383 / ISBN 13: 9780821891384

Editore: American Mathematical Society, US, 2014

This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox''; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last couple of chapters, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book. This book is published in cooperation with Mathematics Advanced Study Semesters. Codice articolo LU-9780821891384

Riassunto:

This textbook is for advanced undergraduate or beginning graduate course, says Levi, and it is not unreasonable to cover two to four of the eight chapters in one semester, so it can be used for more than one course. It covers one degree of freedom, more degrees of freedom, rigid body motion, variational principles of mechanics, classical problems of calculus of variations, the conditions of Legendre and Jacobi for a minimum, optimal control, and the heuristic foundations of Hamiltonian mechanics. He assumes readers have been exposed to beginning courses in physics, in vector calculus, and in basic linear algebra, but does review key concepts when they arise. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

Dati bibliografici

Titolo: Classical Mechanics with Calculus of ...
Casa editrice: American Mathematical Society, US
Data di pubblicazione: 2014
Legatura: Paperback
Condizione: New